Hi
No real need to get a new watch because of this. Why not buy yourself a nice leather strap?
Besides this your question is far too general to answer. There's hundreds of possibilities. If you like to deal with Andrew have a look at his site, choose some models, research them here, then ask specific open questions.
There are some watches that have known functionality flaws, like all seconds at six chronographs. But that you'll find out by reading the reviews on the watch you research. Generally speaking, the more complicated and unusual the model the higher the risk of problems with functionality.
Read around in the brands sections! It's fun and educating at once.
Good luck!
Val.